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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Theoretical analysis of on-chip linear quantum optical information processing networks

Edwin E. Hach, Stefan F. Preble, Jeffrey A. Steidle

Published May 21, 2015• 1 citation
Publisher

Abstract

We present a quantum optical analysis of waveguides directionally coupled to ring resonators, an architecture realizable using silicon nanophotonics. The innate scalability of the silicon platform allows for the possibility of “on-chip” quantum computation and information processing. In this paper, we briefly review a comprehensive method for analyzing the quantum mechanical output of such a network for an arbitrary input state of the quantized, traveling electromagnetic field in the continuous wave (cw) limit. Specifically, we briefly review a recent theoretical result identifying a particular device topology that yields, via Passive Quantum Optical Feedback (PQOF), dramatic and unexpected enhancements of the Hong-Ou-Mandel Effect, an effect central to the operation of many quantum information processing systems. Next, we extend the analysis to our proposal for a scalable, on-chip realization of the Nonlinear Sign (NS) shifter essential for implementation of the Knill-Laflamme-Milburn (KLM) protocol for Linear Optical Quantum Computing (LOQC). Finally, we discuss generalizations to arbitrary networks of directionally coupled ring resonators along with possible applications is the areas of quantum metrology and sensitive photon detection.

DOI
10.1117/12.2177013

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We present a quantum optical analysis of waveguides directionally coupled to ring resonators, an architecture realizable using silicon nanophotonics. The innate scalability of the silicon platform allows for the possibility of “on-chip” quantum computation and information processing. In this paper, we briefly review a comprehensive method for analyzing the quantum mechanical output of such a network for an arbitrary input state of the quantized, traveling electromagnetic field in the continuous wave (cw) limit. Specifically, we briefly review a recent theoretical result identifying a particular device topology that yields, via Passive Quantum Optical Feedback (PQOF), dramatic and unexpected enhancements of the Hong-Ou-Mandel Effect, an effect central to the operation of many quantum information processing systems. Next, we extend the analysis to our proposal for a scalable, on-chip realization of the Nonlinear Sign (NS) shifter essential for implementation of the Knill-Laflamme-Milburn (KLM) protocol for Linear Optical Quantum Computing (LOQC). Finally, we discuss generalizations to arbitrary networks of directionally coupled ring resonators along with possible applications is the areas of quantum metrology and sensitive photon detection.
Silicon nanophotonics show a lot of promise as the basic architecture for quantum information processing devices. This is particularly the case in relation to the scalability of such devices. During this talk I will review our simple theoretical model of a structure that we have identified as a ‘fundamental circuit element’ for linear optical quantum information processing in silicon nanophotonics. In particular, we have shown that, owing to an effect we call Passive Quantum Optical Feedback (PQOF), the topology of this circuit element allows for certain possible operational advantages, in addition to inherent scalability, not expected in bulk linear optics. I will emphasize the extension of our work to larger networks, including the Knill-Laflamme-Milburn (KLM) Controlled-Not (CNOT) gate and its important constituent, the so-called Nonlinear Sign (NS) shifter. Further, I will discuss our ongoing effort to design and optimize scalable networks that seem to have useful applications in quantum metrology and sensing. In developing the discussion, I will examine recent developments related to incorporation of losses and spectral properties in such a way as to generalize our simple, continuous-wave (cw) model of essentially lossless operation. I will also discuss on-chip generation and control of entangled photons within the nanophotonic material itself, especially as related to potentially useful applications in information processing.
Quantum information science aims to revolutionize existing methods for manipulating data by utilizing the unique features of nonclassical physical phenomena. This control is realized over several platforms, one particular being photonics which employs state of the art fabrication techniques that achieve integrated nanocircuit components. The Hong-Ou-Mandel effect underlies the basic entangling mechanism of linear optical quantum computing, and is a critical feature in the design of nanophotonic circuits used for quantum information processing. We will present some results from an on-chip Hong-Ou-Mandel (HOM) experiment that replaces the conventional beam splitter with a more compact and highly versatile ring resonator allowing greater functionality with an expanded parameter space dubbed Hong-Ou-Mandel Manifold (HOMM). The overarching goal of this work is to demonstrate on-chip, scalable, dynamically configurable quantum-optical interconnects for integration into photonic quantum information processing devices.
The emergence of coherent quantum feedback control (CQFC) as a new paradigm for precise manipulation of dynamics of complex quantum systems has led to the development of efficient theoretical modeling and simulation tools and opened avenues for new practical implementations. This work explores the applicability of the integrated silicon photonics platform for implementing scalable CQFC networks. If proven successful, on-chip implementations of these networks would provide scalable and efficient nanophotonic components for autonomous quantum information processing devices and ultra-low-power optical processing systems at telecommunications wavelengths. We analyze the strengths of the silicon photonics platform for CQFC applications and identify the key challenges to both the theoretical formalism and experimental implementations. In particular, we determine specific extensions to the theoretical CQFC framework (which was originally developed with bulk-optics implementations in mind), required to make it fully applicable to modeling of linear and nonlinear integrated optics networks. We also report the results of a preliminary experiment that studied the performance of an in situ controllable silicon nanophotonic network of two coupled cavities and analyze the properties of this device using the CQFC formalism.
Quantum information processing, from cryptography to computation, based upon linear quantum-optical circuit elements relies heavily on the ability offered by the Hong-Ou-Mandel (HOM) effect to ``route'' photons from separate input modes into one of two common output modes. Specifically, the HOM effect accomplishes the path entanglement of two photons at a time such that no coincidences are observed in the output modes of a system exhibiting the effect. In this paper, we prove, in principle, that by operating a specific nanophotonic device properly, one can conditionally ``bunch'' coincident input photons in a way that is more configurable than with an ordinary 50:50 beam splitter, while maintaining the inherent scalability of such an on-chip device.
Here we present a fully quantum mechanical transfer function model for travelling wave whispering gallery mode resonators. Micro-resonators, such as ring and disk resonators, have been key to the development of high performance chip-scale photonic systems due to their compact footprint, sensitivity and low power operation. In this work we present the first understanding of these resonators to any arbitrary multi-photon state. This was achieved by developing a model that utilizes an efficient scheme for determining the quantum electrodynamic transfer functions relating the Bosonic input/output mode operators in the resonator. This approach has been applied to the understanding of both single photon and two-photon states. In this work we will present a key result on a resonant Hong-Ou-Mandel effect that is inherently realized for any resonator-waveguide coupling constants and can operate over a wide range of resonance conditions. Furthermore, the transfer function approach allows for the straightforward understanding of any resonator-waveguide network with arbitrary modes. This will directly enable the application of quantum resonators to the realization of robust, scalable and efficient Linear Optical Quantum Computing (LOQC) gates. Consequently, it is expected that resonators can be used for both Nonlinear Sign Shift and CNOT gates. And these gates can robustly controlled and efficiently tuned using standard electro-optic effects available in a variety of material systems, such as, Silicon.
Chip-scale integrated photonic circuits provide an attractive platform for the implementation of many quantum photonic technologies ranging from precise metrology to secure communication and quantum computation. In particular, silicon photonic platforms support micron-scale nonlinear optical sources of non-classical light which can be mass manufactured using the robust fabrication processes pioneered by the CMOS microelectronics industry. Integration of these quantum photonic sources with high-performance classical photonic devices on the same chip is required for truly scalable quantum information technologies. Integrated nonlinear resonators are investigated as sources of quantum mechanically correlated photon pair sources. An all-order dispersion engineering method is presented as a robust design synthesis for micoring sources. In addition, a novel concept of coupled mode dispersion compensation is proposed and demonstrated, providing significantly improved performance characteristics of resonant four-wave mixing sources. Next a photon pair source is demonstrated in a commercial CMOS microelectronics process opening the door to future integration of quantum photonics with electronic logic and control circuits. Classical nonlinear optical measurements of stimulated four-wave mixing are used for the first time to accurately predict the quantum correlations from the same device operating in the photon pair regime. Next the first demonstration of fully on-chip pump rejection is demonstrated with over 95 dB pump extinction improving the figures of merit from previous demonstrations by multiple orders of magnitude, including losses, detected pair rates and size. Finally, proposals for introducing novel degrees of freedom provided by an integrated platform are presented for further improving the performance of both photon pair and classical nonlinear optical sources.